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3 years ago

Complete y^2+15y+56=(y+7)(y+?) ...?

2 answers:

5 0

The two factors of a quadratic equation can be multiplied to form the original equation. Let the missing term be a:
y² + 15y + 56 = (y + 7)(y + a)
y² + 15y + 56 = y² + (7 + a)y + 7a
We can now compare the coefficient of the like terms, either the one with y or the one without y, and find the value of a.
15 = 7 + a; a = 8
OR
56 = 7a; a = 8

Second factor is (y + 8)

Inessa [10]3 years ago

3 0

y² + 15y + 56 = (y + 7)(y + a)

y² + 15y + 56 = y² + (7 + a)y + 7a

We can now compare the coefficient of the like terms, either the one with y or the one without y, and find the value of a.

15 = 7 + a; a = 8

56 = 7a; a = 8

Second factor is (y + 8)

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25% of 60 to 40% of 30<br> >, < or =

Travka [436]

You can reduce the percentages to fractions:

$25\% = \dfrac{25}{100} = \dfrac{1}{4}$

$40\% = \dfrac{40}{100} = \dfrac{2}{5}$

So, we have

$25\% \text{ of } 60 = \dfrac{1}{4}\cdot 60 = 15$

$40\% \text{ of } 30 = \dfrac{2}{5}\cdot 30 = 12$

5 0

2 years ago

The perimeter of the quadrilateral is 43 centimeters. Find the length of each side.

vesna_86 [32]

Step-by-step explanation:

A quadrilateral is made up of four sides. This means the sum of all the side equals 43. This is given as;

(x + 7) + (x² - 2x ) + (x +3) + (2x - 2) = 43

x² - 2x + 4x + 8 = 43

x² - 2x - 35 = 0

Upon solving for x by factorization;

( x - 5) ( x + 7) = 0

The values of x are; 5 and - 7

Since the side of shape cannot have a negative value, -7 is ignored.

x = 5

The length of the sides are;

- X+7 = 5 + 7 = 12

- x² - 2x = 5² - 2(5) = 25 - 10 = 15

- X+3 = 5 + 3 = 8

2x-2 = 2(5) - 2 = 10 -2 = 8

Check:

8 + 8 + 15 + 12 = 43

7 0

3 years ago

Can the set of lengths be the side lengths of a right triangle?

andreyandreev [35.5K]

Answer:

B. No.

Step-by-step explanation:

We have been given 3 side lengths 7 ft, 12 ft, 17 ft. We are asked to determine, whether the given set of lengths can form a right triangle or not.

We will use Pythagoras theorem to solve our given problem, which states that the square of hypotenuse of a right triangle is equal to the sum of squares of two legs of right triangle.

$17^2=12^2+7^2$

$289=144+49$

$289>193$

Since the sum of squares of both legs is less than square of hypotenuse, therefore, the given set of lengths can not be the side lengths of a right triangle.

4 0

3 years ago

Read 2 more answers

Stanley McBride is employed by the True Blue company. The PPO annual premium is $7,058. His employer pays 70% of the total cost.

Vitek1552 [10]

First deducte his contribution
7,058−7,058×0.70
=2,117.4
Then find weekly deduction
2,117.4÷52
=40.72

4 0

3 years ago

Read 2 more answers

A school has 1500 students. Given that 3% of them were late for school on a particular day, find the no of students who were pun

Setler [38]

Answer: